The field of the invention are micromechanical appliances which include a flexible element. In many cases it is desired to control the oscillation of such an element under the influence of internal and external forces. A typical micromechanical appliance of the kind at which the current invention is aiming, is known as Scanning or Atomic Force Microscopy (SFM or AFM) and methods related to it.
The Atomic Force Microscope as first known from the U.S. Pat. No. 4,724,318 and further described by G. Binnig, C. F. Quate and Ch. Gerber in Phys. Rev. Letters, Vol.56, No.9, March 1986, pp.930-933, employs a sharply pointed tip attached to a spring-like flexible element, typically in form of a cantilever beam, to scan the profile of a surface to be investigated. At the distances involved, minute forces occur between the atoms at the apex of the tip and those at the surface, resulting in a tiny deflection of the cantilever. The forces occurring between a pointed tip and a surface are usually described as van-der-Waals, covalent, ionic, or repulsive core interaction forces.
Applications of the AFM can roughly be divided into two different groups in accordance with the way in which these forces are detected. In the so-called direct or contact mode, a force map of a surface is derived by measuring the deflection of the cantilever. The second mode is characterized by detecting shifts in the resonant frequency of the mechanical vibration of a cantilever. This mode of operation is known as non-contact, "AC", or attractive mode. The non-contact mode results in a force gradient map of a surface. The most commonly used detection method in the non-contact mode, which is known as "slope detection", involves driving the cantilever at a fixed frequency close to its resonance. The resonant frequency of such a cantilever is given by the square root of k/m, wherein m is the effective mass of the lever and k is the effective spring constant. This effective spring constant is defined as being the sum of the spring constant of the (free) cantilever beam plus the gradient of the force at a direction perpendicular to the surface of a sample. A change in this gradient gives rise to a shift in the resonant frequency, and a corresponding shift in the amplitude of the cantilever vibration. In slope detection the signal is derived by measuring this change in amplitude.
The applicability of the slope detection method is limited by the maximum quality factor Q of the cantilever's resonance. It is in principle possible to achieve very high Q values by carefully designing the cantilever and reducing the damping by air. But the high Q value effects adversely the time constant and hence the available bandwidth. The resulting apparatus is for most applications too slow. The disadvantages of the slope detection method lead to a number of attempts to increase the sensitivity through higher Q values without placing any restriction on the bandwidth or the dynamic range. These attempts are characterized by employing the cantilever as the frequency determining element within a feedback oscillator circuitry. T. R. Albrecht et al. describe for example in J. Appl. Phys. 69 (2), Jan. 16, 1991, pp. 668-673, a setup which includes in addition to a conventional force microscope with a bimorph cantilever an oscillator control amplifier and an FM demodulator circuit. A similar scheme is published by U. Durig et al. in J. Appl. Phys. 72(5), Sep. 1, 1992, pp. 1778-1798. Therein the resonant frequency of the cantilever is detected by means of a Phase Locked Loop (PLL) phase/frequency detector. The output of the PLL circuit is also used after an appropriate phase shifting and amplifying to excite the vibration amplitude of the cantilever as to maintain a constant level. The invention strives to improve these solutions without giving up the inherent advantages of not requiring a quantitative measurement of the cantilever's deflection and of maintaining its oscillation at a constant amplitude.